From a group of eight people how many different committees : DS Archive
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# From a group of eight people how many different committees

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Manager
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From a group of eight people how many different committees [#permalink]

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08 Aug 2003, 00:07
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From a group of eight people how many different committees of four or five people each can be arranged?
Manager
Joined: 10 Jun 2003
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08 Aug 2003, 07:33
Committee of four: 8C4 = 70
Committee of five: 8C5 = 56

Then four or five would be 70 + 56 = 126
Senior Manager
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12 Feb 2004, 19:20
Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks
Director
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12 Feb 2004, 20:09
gmatblast wrote:
Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks

Could you explain the reason for multiplying by 2?
Director
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13 Feb 2004, 01:39
Why not 350? 8C4=70, choose one more from the rest 4 to form a five member committee or 70x4=280-5 member committees and 70-4 memeber or 350 in total.
Senior Manager
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13 Feb 2004, 06:55
gmatblast wrote:
Shouln't the answer be 8C4 * 2 + 8C5 ?

The question is asking for number of committees Not the number of ways to form the committees

Thanks

Could you explain the reason for multiplying by 2?

That was my mistake!! We do not need to multiply by 2.

I overthought the problem. I thought that the question is asking for number of committees Not the number of ways to form the committees

So I thought when we select any 4 people out of 8 to form a commitee, we are basically creating 2 committees. 4 selected people and 4 remaining. So we need to multiply 8C4 by 2. But I now know that 8C4 will cover all the remaining people as well.

So no need to multiply by 2.
13 Feb 2004, 06:55
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